Both of your examples could be used with a different meaning, but "arguably" is more braodly used than "unarguably".
Each word of the English language has its specific purpose or meaning when people choose to use it.
Arguably is defined as a "sentence adverb" which means:
It may be argued (used to qualify the statement of an opinion or
belief): ‘she is arguably the greatest woman tennis player of all
People argue because each has a different point of view and way of judging something or someone. If you use "arguably" in a sentence, you are admitting that "what you are stating" can be a topic of argument as the above example explains. Some people may think Martina Navratilova is the best female tennis player "ever", others may think Stefanie Graf is the one. It is arguable and it will "arguably" take years to reach a conclusion. There might be "no" end of this argument at all because it is your preference and how you view their records.
You use "arguably" when:
You know there could arise an argument because you know your statement is controversial and people might have a differnt view/idea about it.
You want to avoid any argument about this topic.
When you Google search "arguably best", "unarguably best", you get 182,000 hits for the former and only 6,890 hits for the latter. If you Google "unarguably worst", you get merely 274 hits, but 30,400 hits for "arguably worst".
You can't depend on the number of hits, but you can see "unarguably" is far less used than "arguably".
Adverbs like "absolutely", "certainly", and "surely" are far more frequently used than "unarguably". The reason why is arguable but you "arguably" don't want to use an "unpopular" adverb among many (which can mean the same) when you make a statement.